Independent solution

How to solve this Prospective Loan Balance question

Setup

Setup

Immediately after payment 40, twenty declining monthly payments remain. The monthly yield is 0.09/12, and payment t is 1,000(0.98) to the power t−1.

Pt=1000(0.98)t−1,j=0.09/12P_t=1000(0.98)^{t-1},\quad j=0.09/12

Model

Model

Use the prospective method: discount payments 41 through 60 back to time 40. Keeping the original payment index in the formula preserves the correct 2% decline already realized.

B40=∑t=41601000(0.98)t−1(1+j)−(t−40)B_{40}=\sum_{t=41}^{60}1000(0.98)^{t-1}(1+j)^{-(t-40)}

Compute

Compute

The twenty discounted terms sum to 6,888. Rounding to the precision of the alternatives gives 6,890.

B40=6888B_{40}=6888

Answer

Answer

The calculation gives 6890 for prospective loan balance, matching published choice B.

B40=6890(B)\boxed{B_{40}=6890\quad\text{(B)}}